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Bouchaud's model exhibits two different aging regimes in dimension one

Gerard Ben Arous·Jiri Cerny
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Abstract

Let E_i be a collection of i.i.d. exponential random variables. Bouchaud's model on Z is a Markov chain X(t) whose transition rates are given by w_{ij}=ν\exp(-β((1-a)E_i-aE_j)) if i, j are neighbors in Z. We study the behavior of two correlation functions: P[X(t_w+t)=X(t_w)] and P[X(t')=X(t_w) \forall t'\in[t_w,t_w+t]]. We prove the (sub)aging behavior of these functions when β>1 and a\in[0,1].

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Gerard Ben Arous, Jiri Cerny. 2005-05-20. Bouchaud's model exhibits two different aging regimes in dimension one. https://doi.org/10.1214/105051605000000124

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